Find
f(a),f (a+h)and the difference quotient, f(a + h) − f(a) over h , where h not 0
f(x) = 4x2 + 18
f(x) = 4a2 + 18
f(a + h) = 4(a + h)2 + 18 = 4(a2 + 2ah + h2) + 18 = 4a2 + 8ah + 4h2 + 18
[ f(a +h) - f(a) ] / h = [ (4a2 + 8ah + 4h2 + 18) - (4a2 + 18) ] / h
= [ 4a2 + 8ah + 4h2 + 18 - 4a2 - 18 ] / h
= [ 8ah + 4h2 ] / h
= 8a + 4h